It's easy! If the CIA says one thing and former Sen. Graham says another, then the CIA is lying. Or, "in error," if you prefer.
(Background here and here, in which Graham says that some of the briefings in which he was allegedly filled in about waterboarding and related techniques never occurred. This matters, because the CIA's claims are part of the same argument that Nancy Pelosi and other Democrats in Congress had known about and acquiesced to waterboarding all the way along.)
Part of the payoff of reaching age 72 and having spent 38 years in public office, as Graham has, is that people have had a chance to judge your reputation. Graham has a general reputation for honesty. In my eyes he has a specific reputation for very good judgment: he was one of a handful of Senators actually to read the full classified intelligence report about the "threats" posed by Saddam Hussein. On the basis of reading it, despite a career as a conservative/centrist Democrat, he voted against the war and fervently urged his colleagues to do the same. "Blood is going to be on your hands," he warned those who voted yes.
More relevant in this case, Graham also has a specific reputation for keeping detailed daily records of people he met and things they said. He's sometimes been mocked for this compulsive practice, but he's never been doubted about the completeness or accuracy of what he compiles. (In the fine print of those records would be an indication that I had interviewed him about Iraq war policy while he was in the Senate and recently spent time with him when he was on this side of the world.)
So if he says he never got the briefing, he didn't. And if the CIA or anyone acting on its behalf challenges him, they are stupid and incompetent as well as being untrustworthy. This doesn't prove that the accounts of briefing Pelosi are also inaccurate. But it shifts the burden of proof.